Bounds for the Thermal Conductance of Body of Rotation
(*) Corresponding author
DOI: https://doi.org/10.15866/iremos.v13i3.18619
Abstract
A mathematical heat transfer model is developed for the steady-state heat transfer through a homogeneous isotropic body of rotation. The developed model is used to obtain estimations for two-sided thermal heat transfer conductance in case of a special type of body of rotation. The body of rotation considered is bounded by the coordinate surfaces of an orthogonal curvilinear coordinate system. The equations of the Fourier’s theory of heat conduction in solid body are used to formulate the corresponding thermal boundary value problem. The studied steady-state heat conduction problem is axisymmetric. The determination of the heat flow is based on the concept of the thermal conductance the inverse of which is the thermal resistance. The exact (strict) value of thermal conductance is known only for bodies with very simple shapes, therefore, the principles and the methods that can be used for creating lower and upper bounds to the numerical value of thermal conductance are important. The derivation of the upper and the lower bound formulae for the heat conductance of axisymmetric ring-like body is based on the two types of Cauchy–Schwarz inequality. The condition of equality of the derived lower and upper bounds is examined. Several examples illustrate the applications of the derived upper and lower bound formulae. The presented method can be used not only for the estimation of thermal conductance. For example, similar formulation can be given to obtain two-sided bounds for the electrical resistance of solid body conductor in the case of spatially steady flow of electric charges.
Copyright © 2020 Praise Worthy Prize - All rights reserved.
Keywords
Full Text:
PDFReferences
Fakir, M., Khatun, S., Two-Dimensional Heat Transfer Through Long-Wide Insulated-Tip Thin Rectangular Fin: a Comparative Study, (2017) International Review of Aerospace Engineering (IREASE), 10 (3), pp. 167-173.
https://doi.org/10.15866/irease.v10i3.12469
Sowayan, A., Hasani, S., Analysis of Conductive, Convective and Radiative Heat Transfer in Longitudinal Fins of Variable Profiles, (2019) International Review of Mechanical Engineering (IREME), 13 (9), pp. 523-532.
https://doi.org/10.15866/ireme.v13i9.17743
I. Ecsedi, A Method of Estimating the Rate of Heat Flow, Alkalmazott Matematikai Lapok, Vol. 5(Issue 3-4):241-247, 1979. (In Hungarian with English summary).
I. Ecsedi, The Investigation of a Problem of Heat Transfer, Alkalmazott Matematikai Lapok, Vol. 6(Issue 3-4):337-344, 1980. (In Hungarian with English summary).
I. Ecsedi, Mean Value and Bounding Formulae for Heat Conduction Problems, Archives of Mechanics, Vol. 54(Issue 2):127-140, 2002.
R. Wojnar, Upper and Lower Bounds on Heat Flux, Journal of Thermal Stresses, Vol. 21(Issue 3-4):381-403, 1998.
https://doi.org/10.1080/01495739808956153
I. Ecsedi, Bounds for the Effective Heat Conduction Coefficient, Mechanics Research Communications, Vol. 29(Issue 2-3):189-193, 2002.
https://doi.org/10.1016/s0093-6413(02)00238-0
H.S. Carslaw, I.C. Jaeger, Conduction of Heat in Solids (Second Edition, Clarendon Press, Oxford, 1986).
M. Jacob, Heat Transfer, Vol I.–Vol II. (Wiley, New York, 1949).
N.M. Özişik, Boundary Value Problem of Heat Conduction (Dover Publication, New York, 1989).
I. Ecsedi, A. Baksa, Estimation of Heat Flow in Circular Bars of Variable Diameter, Journal of Computational and Applied Mechanics, Vol. 13(Issue 1):5-14, 2018.
https://doi.org/10.32973/jcam.2018.002
I. Ecsedi, Bounds for the Heat Transfer Coefficient, Acta Technica Academiae Scientiarum Hungarica Vol. 95(Issue 1-4): 21-31, 1982.
H.G. Elrod, Two Simple Theorems for Establishing Bounds on the Total Heat Flow in Steady-State Heat-Conduction Problems with Convective Boundary Conditions, Journal of Heat Transfer, Vol. 96(Issue 1): 65-70, 1974.
https://doi.org/10.1115/1.3450142
A.G. Ramm, Estimation of Thermal Resistance for Bodies of Complex Shape, Journal of Engineering Physics, Vol. 13(Issue 6): 485-488, 1967.
https://doi.org/10.1007/BF00828978
V.S. Zarubin, G.N. Kuvyrkin, I.Y. Savelyeva, Two-Sided Thermal Resistance Estimates for Heat Transfer Through an Anisotropic Solid of Complex Shape, International Journal of Heat and Mass Transfer, Vol. 116(Issue 1):833–839, 2018.
https://doi.org/10.1016/j.ijheatmasstransfer.2017.09.054
R. Weinstock, Calculus of Variations (McGraw-Hill, New York, 1952).
P.K. Chattopadhyay, Mathematical Physics (New Age International Ltd. Publishers, New Delhi, 2004).
G. Sidebotham, Heat Transfer Modeling. An Inductive Approach. (Springer, New York, 2015).
J.H. Lienhard IV, J.H. Lienhard V, A Heat Transfer Textbook. (Phlogiston Press, Cambridge, Massachusetts, 2008).
B. Nagappan, K. Alagu, Y. Devarajan, Heat Transfer Enhancement of a Cascaded Thermal Energy Storage System with Various Encapsulation Arrangements, Thermal Science, Vol. 23(Issue 2A):823-833, 2019.
https://doi.org/10.2298/tsci160926227n
S. Nekahi, K. Vaferi, M.Vajdi, F.S. Moghanlou, M.S. Asl, M. Shokouhimehr, A Numerical Approach to the Heat Transfer and Thermal Stress in a Gas Turbine Stator Blade Made of HfB2, Ceramics International, Vol. 45(Issue 18):24060-24069, 2019.
https://doi.org/10.1016/j.ceramint.2019.08.112
V.I. Zinchenko, V.D. Goldin, V.G Zverev, Investigations of Heat and Mass Transfer for Thermal Protection Materials in a Long Flight, Journal of Applied Mechanics and Technical Physics Vol. 59(Issue 2):281-291, 2018.
https://doi.org/10.1134/s0021894418020116
R.M.S. Gama, An a Priori Upper Bound Estimate for Conduction Heat Transfer Problems with Temperature-Dependent Thermal Conductivity, Mechanics Research Communications, Vol. 92: 87-91, 2018.
https://doi.org/10.1016/j.mechrescom.2018.08.002
M.A. Hassab, M.K. Mansour, M.M.M. Sorour, Thermal Investigation of the Conjugate Heat Transfer Problem in Multi-Row Circular Minichannels, Numerical Heat Transfer Part A: Applications, Vol. 71(Issue 12): 1205-1222, 2017.
https://doi.org/10.1080/10407782.2017.1353369
Bounouar, A., Gueraoui, K., Taibi, M., Lahlou, A., Driouich, M., Sammouda, M., Men-La-Yakhaf, S., Belcadi, M., Numerical and Mathematical Modeling of an Unsteady Heat Transfer within a Spherical Cavity: Applications Laser in Medicine, (2017) International Review of Civil Engineering (IRECE), 8 (4), pp. 187-195.
https://doi.org/10.15866/irece.v8i4.12429
Bounouar, A., Gueraoui, K., Taibi, M., Driouich, M., Rtibi, A., Belkassmi, Y., Zeggwagh, G., Mathematical and Numerical Modeling of an Unsteady Heat Transfer within a Spherical Cavity: Laser Interaction with Human Skin, (2018) International Review of Civil Engineering (IRECE), 9 (5), pp. 209-217.
https://doi.org/10.15866/irece.v9i5.14666
Refbacks
- There are currently no refbacks.
Please send any question about this web site to info@praiseworthyprize.com
Copyright © 2005-2024 Praise Worthy Prize